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anonymous

  • 5 years ago

What mathematical induction?

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  1. anonymous
    • 5 years ago
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    series of natural numbers

  2. anonymous
    • 5 years ago
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    But, I no get (k+1) part

  3. amistre64
    • 5 years ago
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    proving that if its true for one step; its true for every step

  4. anonymous
    • 5 years ago
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    for me you have to identify whta is the successor of 1, and it is 0, so 1 is the successor of k

  5. anonymous
    • 5 years ago
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    oops sorry

  6. anonymous
    • 5 years ago
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    So, if n=1 is true, then (k+1) should be true?

  7. anonymous
    • 5 years ago
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    No.

  8. amistre64
    • 5 years ago
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    you havent really asked that detailed of a question; youre keeping secrets

  9. anonymous
    • 5 years ago
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    The series of natural numbers, can all be defined if we know what we mean by the three terms "0," "number", and "successor." But we may go a step farther: we can define all the natural numbers if we know what we mean by "0" and "successor." It will help us to understand the difference between finite and infinite to see how this can be done, and why the method by which it is done cannot be extended beyond the finite. We will not yet consider how "0" and "successor" are to be defined: we will for the moment assume that we know what these terms mean, and show how thence all other natural numbers can be obtained.

  10. watchmath
    • 5 years ago
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    Have you seen a domino effect? that's how you should think about induction.

  11. anonymous
    • 5 years ago
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    Oops, didn't know you needed example. I sorry :) I give you example :) One moment, please

  12. anonymous
    • 5 years ago
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    1 + 2 + 3 + . . . + n = ½n(n + 1)

  13. anonymous
    • 5 years ago
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    The logic is: It's true for n= (for example) 1 AND you can prove truth for n=k implies truth for n=k+1) THEN It's true for n = 1, 2, 3.....

  14. amistre64
    • 5 years ago
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    n(n+1) ------ ah yes 2

  15. amistre64
    • 5 years ago
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    gausses fame..

  16. anonymous
    • 5 years ago
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    [Oh fun fact that isn't why Gauss is famous]

  17. watchmath
    • 5 years ago
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    Translating INewton logic into domino logic: How to make all the domino fall. 1) Make sure the 1st domino fall. 2) Make sure that whenever the kth domino fall, the (k+1)th domino fall as well. If you can ensure that then all dominos will fall :).

  18. amistre64
    • 5 years ago
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    n=2; 1+2 = 3 ; 2(2+1)/2 = 3

  19. anonymous
    • 5 years ago
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    ............ THAT GREAT IDEA!!!!! :DDDDD

  20. amistre64
    • 5 years ago
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    its why I know gauss tho lol

  21. amistre64
    • 5 years ago
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    n = 3; 1+2+3 = 6 ; 3(3+1)/2 = 12/2 = 6

  22. anonymous
    • 5 years ago
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    Gauss Fact #1: Erdos believed God had a book of all perfect mathematical proofs. God believes Gauss has such a book.

  23. anonymous
    • 5 years ago
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    Gauss field equations

  24. anonymous
    • 5 years ago
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    Gauss Fact #2: Gauss checked the infinity of primes by counting them, starting from the last. Gauss Fact #3: Gauss considers infinity as the first non-trivial case in a proof by induction.

  25. anonymous
    • 5 years ago
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    \[ \text{Assume } \sum^k_{r=1}r = \frac{k(k+1)}{2}\] \[ \text{Assume } \sum^{k+1}_{r=1}r = \sum^k_{r=1}r + (k+1) = \frac{k(k+1)}{2} + (k+1) = \frac{k(k+1)+2(k+1)}{2} \] \[=\frac{(k+1)[(k+1)+1]}{2} \] By mathematical induction blah...

  26. watchmath
    • 5 years ago
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    I think the second word of "assume" shouldn't be there.

  27. anonymous
    • 5 years ago
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    It shouldn't, lazy copy and past, ugh.... sorry.

  28. anonymous
    • 5 years ago
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    paste*. I should have used \[\implies \] to start that line.

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